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Proof step 18 from proof mult-dist (previous step)

⊦ mkDecimal(i * (i1 * 10 ^ abs(i4) + i3 * 10 ^ abs(i2)), abs(i0) + abs(i2) + abs(i4)) = mkDecimal((i * i1) * 10 ^ abs(abs(i0) + abs(i4)) + (i * i3) * 10 ^ abs(abs(i0) + abs(i2)), abs(abs(i0) + abs(i2)) + abs(abs(i0) + abs(i4)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
⊦ mkDecimal(i * (i1 * 10 ^ abs(i4) + i3 * 10 ^ abs(i2)), abs(i0) + abs(i2) + abs(i4)) = mkDecimal(i * i1 * 10 ^ (abs(i0) + abs(i4)) + i * i3 * 10 ^ (abs(i0) + abs(i2)), 2 * abs(i0) + abs(i2) + abs(i4))

Rule argument

Additional information

Used simplifier rules: add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%abs-abs-01: ⊦ abs(abs(i) + abs(j)) = abs(i) + abs(j); from specification int-abs